Planar subgraphs and planarization play an important role for the
study of many classes of beyond-planar graphs
[1]}. This may indicate that beyond-planar
graphs are close to planar graphs, i.e., they are “nearly planar”
[2]}. A major distinction comes from subdivisions.
Clearly, every graph \(G\)  has a subdivision that is 1-planar. On
the other hand, a graph is planar if and only if its subdivision is
planar.
